What kind of wave is associated with particles , in wave particle duality?

I know It is not EM wave.
It is not probablity wave since probablity can never be negative.

But I think De Broglie's wave length for particles (like electron) is derived using equation of mass-energy equivalence. It infers that this wave carries energy ;for this wave-length is same as that of EM energy equivalent to the particle (E=mc^2). Certainly the particle is not spontaneously changing to EM wave then again this EM wave somehow give rise to a particle.
So why have we used this equation to find the wave nature of particle? What is it's significance?
#Electron is both particle and wave.
What kind of wave?

It is a naive question from a novice and ignorant person, interested in quantum physics. please respond.

Staff: Mentor

We don't know what the quantum mechanical wave function is, in the sense that you seem to be looking for. All we know is what we can do with it: multiply it with its complex conjugate and use it as the particle's probability density: [itex]P(x) = \psi^*(x) \psi(x)[/itex].

Different people have different opinions about what [itex]\psi[/itex] "really" is or represents, that is, they favor different interpretations of quantum mechanics. All serious interpretations reduce ultimately to the same mathematics, because the standard mathematics of QM makes predictions that agree very well with experiment. There is as yet no way to distinguish between these interpretations by experiment. All people can do is argue about which interpretation is better. Probably most of the posts in this forum are connected with these arguments.

Actually, I think this is a simpler question than it appears. The question that appears in the topic is:

What kind of wave is associated with particles , in wave particle duality?

The "wave" in the wave-particle duality isn't really a wave, but rather the behavior that is consistent with what we know from classical wave. So the "wave" in wave-particle duality is more of the observation of diffraction, interference, etc. which are all wave behavior. So essentially, it isn't really a description of the system, but rather a description of the observation.

Thanks for prompt response jtbell.
Now please say what this wave-length really is?
If this is a question with no meaning then please interpret it in mathematics (better with explanation- i'am not a physics student).

Ahmed Abdullah: the wave has an amplitude, which can be negative. And you are right that probability can't be negative. However, have you heard that the wavefunction is representing the probabilty AMPLITUDE. In order to get a quantity, say probability, is to take the amplitude modulus square.

The same thing is for light, the intensity is the modulus square of the amplitude, the amplitude can be negative. And in QM, the amplitude can even be complex-valued.

Staff: Mentor

But I think De Broglie's wave length for particles (like electron) is derived using equation of mass-energy equivalence. It infers that this wave carries energy ;for this wave-length is same as that of EM energy equivalent to the particle (E=mc^2).

No, the wavelength of [itex]\psi[/itex] is related to the momentum of the particle: [itex]\lambda = h / p[/itex]. The momentum is related to the mass and energy of the particle by [itex]E^2 = (pc)^2 + (mc^2)^2[/itex].

No, the wavelength of [itex]\psi[/itex] is related to the momentum of the particle: [itex]\lambda = h / p[/itex]. The momentum is related to the mass and energy of the particle by [itex]E^2 = (pc)^2 + (mc^2)^2[/itex].

Oh i got it. Electron has different wavelengths in different energy levels.
The equation suggests; the higher the energy level the lower the wavelength is.

The wave associated with a particle is independent of charge of the particle .Whether the particle is negative or positive or neutral the wave associated with is same . But it depends on the Mass of the particle.If the particle is heaveir the particle has less velocity so position of particle can be determined and their is uncertainity in momentum and vice versa.i.e if the mass is less velocity is more.